Characterization of Compact Subsets of A^p with Respect to Weak Topology

2008/04/17 by Hirbod Assa, Assa, Hirbod
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.0804.2873

8 pages

arxiv created 2008/04/17 · arxiv updated 2009/12/01

Abstract

In this brief article we characterize the relatively compact subsets of A^p for the topology σ(A^p,R^q) (see below), by the weak compact subsets of L^p . The spaces R^q endowed with the weak topology induced by A^p, was recently employed to create the convex risk theory of random processes. The weak compact sets of A^p are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on R^q and for their use in the optimization theory.

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